Evangelou, E., Zhu, Z. and Smith, R.L. (2011) Estimation and Prediction for Generalized Linear Mixed Models Using High-Order Laplace Approximation. Journal of Statistical Planning and Inference, 141, 3564-3577.
https://doi.org/10.1016/j.jspi.2011.05.008

has been cited by the following article:

• TITLE: Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties

  AUTHORS: Dan Gabriel Cacuci

  KEYWORDS: Fourth-Order Predictive Modeling, Data Assimilation, Data Adjustment, Uncertainty Quantification, Reduced Predicted Uncertainties

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.13 No.4, October 16, 2023

  ABSTRACT: This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.